I hope these tips help you navigate Singapore as smoothly as possible.
Taxi/Uber/Grab
There is no Uber in Singapore, its equivalent is called Grab. I suggest to download and set up the app before travelling, it's easy but takes a few minutes to complete all the details.
With Grab you have the option to book a "family-car": These cars can provide a child seat (1-4 years) or a booster (4-7 years). For Grab it is mandatory that your toddler is in a seat. Taxis do not have this option, yet it's also not mandatory to have your child in a child seat. If you are happy to have them on your lap, you can do so.
If you have a Ride Safer vest, you're allowed to use them in Singapore.
Public Transport
Singapores public transport is reliable, clean and fairly easy to use. Even in rush hour there is usually enough space to get on with a stroller.
Simply tap your contactless credit card when boarding and again when getting off and your fare will be calculated automatically. Kids up to 7 years of age ride for free and for older kids you can buy a kids travel card at any metro station. (S$10 incl. S$5 travel credit)
Be aware that you're not allowed to eat or drink in stations and on buses/trains, Singapore enforces hefty fines.
Singapore offers many fantastic playgrounds, both indoor and outdoor.
Outdoor playgrounds offer toilets and drinking water nearby and are built to entertain every age. Some of them feature lovely splash areas.
Indoor playgrounds can be a great way to cool off a bit from the heat, if your little one is not used to it. Be aware that indoor playgrounds require you to book a specific slot. The more popular ones sell out quickly, especially on the weekend.
Check out my map of top places on the left.
Singapore's family facilities are absolutely fantastic! In newer facilities you'll always find a family restroom with a changing table, enough space for you, the family and a stroller. It is not uncommon to also find a kid toilet and a lower kids sink.
The family rooms are often combined with dedicated nursing rooms, though less common.
There are many places where one (female) stall is marked with a kid: this stall has a safe seat for your baby and generally a built in toddler toilet seat. It's less common for male toilets in my experience but again, there are the family rooms.
On the other hand, in neigbourhoods with mainly older, more traditional buildings or small restaurants in shophouses, changing tables are much more rare. (eg. Chinatown, Kampong Glam)
Look for a (preferably newer) shopping mall in these areas to change your little ones.
Being the multi-cultural city it is, you find all kinds of cookies/crackers/etc. Check out ColdStorage or Little Farms for a large choice of "western" snacks. Our toddler particularly loved corn cakes and those took us a while to find: If your kid has a strong preference for one snack, pack enough just to give you a few days to find them, if needed. I mean, I probably don't need to tell any parent to pack snacks. But yea.